A Note on Two Constructions of Zero-Difference Balanced Functions
This is an incremental theoretical contribution to combinatorial design and coding theory, with potential applications in cryptography and communications.
The paper presents two constructions of zero-difference balanced (ZDB) functions, obtaining them over a specific algebraic structure and showing that known cyclotomic coset-based ZDB functions are special cases of a generic construction, with applications also discussed.
Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over $\mathbb{Z}_{e}\times \prod_{i=0}^{k}{\mathbb{F}_{q_i}}$ are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over $\mathbb{Z}_{n}$ are special cases of a generic construction. Moreover, applications of these ZDB functions are presented.